coincidence

Coincidence algorithm

Since R2021a

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Syntax

x = coincidence(res,div,maxval)
x = coincidence(res,div,maxval,tol)

Description

x = coincidence(res,div,maxval) returns the scalar x that is less than or equal to maxval and is congruent to each remainder in res for the corresponding divisor in div. x satisfies

mod(x,div) = res.

In other words, dividing x by each element of div leaves as remainder the corresponding element of res.

example

x = coincidence(res,div,maxval,tol) also specifies the tolerance. In practice, there may be no value that satisfies all constraints in res and div exactly. In that case, coincidence identifies a set of candidates that approximately satisfy the constraints and are within an interval of width 2 × tol centered at the candidates' median. The function then returns the median as x.

Examples

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Open Live Script

Find a number smaller than 1000 that has a remainder of about 12 when divided by 19, a remainder of about 13.1 when divided by 20.4, and a remainder of about 6.1 when divided by 11.

There is no number that satisfies the constraints exactly, so specify a tolerance of 1.

rems = [12 13.1 6.1];
divs = [19 20.4 11];

tol = 1;

x = coincidence(rems,divs,1000,tol)
x = 
809.1000

Verify that the true remainders are within the specified tolerance.

tr = x - floor(x./divs).*divs
tr = 1×3

   11.1000   13.5000    6.1000

Repeat the computation, but now specify a tolerance of 3. The number that satisfies the constraints decreases as the tolerance increases.

tol = 3;

x = coincidence(rems,divs,1000,tol)
x = 
31

tr = x - floor(x./divs).*divs
tr = 1×3

   12.0000   10.6000    9.0000

Increase the tolerance to 6. The tolerance has to be smaller than the smallest specified remainder.

tol = 6;

x = coincidence(rems,divs,1000,tol)
x = 
12

tr = x - floor(x./divs).*divs
tr = 1×3

    12    12     1
Open Live Script

In a staggered pulse repetition frequency (PRF) radar system, the first PRF corresponds to 70 range bins and the second PRF corresponds to 85 range bins. The target is detected at bin 47 for the first PRF and bin 12 for the second PRF. Assuming each range bin is 50 meters, compute the target range from these two measurements. Assume the farthest target can be 50 km away. 

idx = coincidence([47 12],[70 85],50e3/50);
r = 50*idx
r = 
30350

Input Arguments

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Remainder array, specified as a row vector of nonnegative numbers. res must have the same number of elements as div.

Data Types: single | double

Divisor array, specified as a row vector of positive numbers. div must have the same number of elements as res.

Data Types: single | double

Upper bound, specified as a positive scalar.

Data Types: single | double

Tolerance, specified as a nonnegative scalar. tol must be smaller than the smallest element of res.

Data Types: single | double

Output Arguments

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Congruent value, returned as a scalar.

Extended Capabilities

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C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a

See Also

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